SHORT CIRCUIT CHARACTERISTICS IN ELECTRICAL NETWORKS

ABSTRACT

In this article, short circuits occurring in medium and low voltage distribution networks are studied. In it, the situation, effects and damages of short circuits in electrical networks are considered based on switching schemes.

АННОТАЦИЯ

В данной статье исследуются короткие замыкания, возникающие в распределительных сетях среднего и низкого напряжения. В ней рассматривается ситуация, последствия и повреждения коротких замыканий в электрических сетях на основе коммутационных схем.

Keywords: short-circuit, electrical networks, consumer, short-circuit performance characteristics.

Ключевые слова: КЗ, электрические сети, потребитель, КЗ.

Short-circuit

In this case, the consumer resistance is short-circuited by a fault (by metal or by arcing) so that a very high line current flows. A distinction must be drawn between symmetrical (three-pole) and asymmetrical (one or two-pole) short circuits. Only the three-pole fault can be represented in the single-phase equivalent circuit diagram. That is why only this type of fault is examined in the following experiment. When a short-circuit occurs, the transmitted power is generally much greater than the thermal limit rating of the transmission line. The faulty condition must thus be recognized by the network protection device and switched off within the shortest possible time. In order to better understand these three operating cases, they are to be graphically displayed in the form of a vector or phasor diagram. In general, vector diagrams are used for networks operated with sinusoidal voltages in order to better illustrate the processes.

The representation of an AC quantity as a vector makes two statements about this quantity: namely about the value (vector length) and the phase relation (vector direction). The sinusoidal curve of the quantity can be recorded as a projection of the rotating point of the vector on the ordinate of the coordinate system; the angular velocity ω is equal to the circuit frequency 2πf of the oscillation. Expressed the other way round, a vector represents a snapshot of a sinusoidal phenomenon. Vectors can be geometrically added and subtracted, thus allowing, e.g., the voltage drops in a network to be easily illustrated. In this connection, the use of the complex calculations in which the vectors are shown in the Gaussian plane is favourable. By multiplication by the complex operator j, for example, a 90° rotation of a vector is achieved. However, complex representations are used here only when the relationships shown in the vector diagrams are to be evaluated mathematically. One vector is selected arbitrarily as the reference vector with the phase angle 0°. All other angles in the vector diagram are with reference to this. For practical reasons, the voltage vector at the line end is selected as the reference vector when representing the operating performance of a transmission line.

The following illustrations show the single phase equivalent circuit diagram of a loss-free transmission line in the operating cases described above with the currents, voltages and voltage drops indicated; the respective combined voltage and current vector diagram is included. The following uniform indices are used for the representations:

Figure 1. Single-phase equivalent circuit diagram of a loss-free three-phase transmission line in no-load operation, with appropriate vector diagram

Beginning of line  point 1

End of line            point 2

Neutral point        point 0

With regard to the experiment procedure, it must be mentioned that the relationships barely change when studying low-loss transmission lines, as the effective resistance R of the high and ultra-high voltage lines is equal to approximately 10% of the reactance X = ωL in the most un favourable case. Due to the geometric addition of the voltage drops, the mathematical treatment becomes much more complex, while the results deviate insignificantly from those determined through the study of a loss free transmission line. In order not to lose sight of what is important, the following derivations refer to the loss-free transmission line. Deviations in the performance of real, i.e. low-loss transmission lines are noted in the appropriate places.

Short-circuit performance characteristics

Figure 2. Single-phase equivalent circuit diagram of a loss-free three-phase transmission line with short-circuit and coresponding vector diagram

In this type of operation, the transmission line is short-circuited at the end, i.e. I₂ = I₁₂ and U₂ = 0. The current I₁ at the beginning of the transmission line results from the geometric addition of the currents I₁₀ through the operating capacitance C_B/2 at the beginning of the line and I₁₂ through the line inductor. The phase angle ω₁ between U₁ and I₁ is exactly 90°; for low-loss transmission lines, it is still about 85°.

In the experiment procedure the three operating cases described above are simulated first. Afterwards the performance of the transmission line model is investigated for mixed ohmic-inductive and a mixed ohmic-capacitive load.

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